Schubert polynomials

In mathematics, Schubert polynomials are generalizations of Schur polynomials that represent cohomology classes of Schubert cycles in flag varieties. They were introduced by Lascoux & Schützenberger (1982) and are named after Hermann Schubert.

Lascoux (1995) described the history of Schubert polynomials.

The Schubert polynomials ${\displaystyle {\mathfrak {S}}_{w}}$ are polynomials in the variables ${\displaystyle \ x_{1},x_{2},\ldots }$ depending on an element ${\displaystyle w}$ of the infinite symmetric group ${\displaystyle S_{\infty }}$ of all permutations of ${\displaystyle 1,2,3,\ldots }$ fixing all but a finite number of elements. They form a basis for the polynomial ring ${\displaystyle \mathbb {Z} [x_{1},x_{2},\ldots ]}$ in infinitely many variables.

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